The Scotland Under-21 international defender rose in a crowded goalmouth to head home a cross from Michael Kightly three minutes into stoppage time.
It earned Wolves a second successive home win but was rough on Coventry boss Iain Dowie and his players.
Coventry, who had ended a run of four league games without a win against Blackpool on Tuesday, should have made it back-to-back victories.
They had enough chances, especially in the second half, to have raced to a comfortable win.
But a dogged defensive display by Wolves and some vital saves by substitute goalkeeper Graham Stack kept Coventry at bay and paved the way for the late heroics from Collins.
Coventry should really have made an early breakthrough as Wolves only came to life as an attacking force in the final five minutes of the first half.
But Michael Mifsud was denied by a smart save from Wayne Hennessey before Robbie Simpson shot weakly and wide after Dele Adebola had chested the ball into his path.
Wolves then lost left-back Michael Gray and Hennessey with hamstring and hip problems in the space of ten minutes before finally making their mark in attack.
Michael Kightly was the spearhead for Wolves and it needed a smart save from Andy Marshall to deny him in the 40th minute.
Kightly then had a goalbound drive deflected away for a corner by Stephen Hughes five minutes later.
The interval came at the wrong time for Wolves and they could not retain the initiative at the start of the second period.
Coventry peppered the Wolves goal but could not find a way through a resolute rearguard. Simpson and Michael Mifsud were both frustrated by Stack.
Simpson was then denied a goal by a last-ditch challenge from Jody Craddock before Hughes had his free-kick blocked.
Skipper Michael Doyle crucially wasted a golden chance to finally break the deadlock 12 minutes from time.
The Irishman was picked out by a great cross-field ball from Jay Tabb and only had Stack to beat but pulled his angled drive across the face of goal.
It was to prove to be a costly miss thanks to the later heroics of Collins.